What term is used for a rank higher than a 1st Dan?

The correct term for a rank higher than a 1st Dan is typically referred to in the form of "2nd Dan." This denotes the next level of advancement in many martial arts systems. Dan ranks are numerical representations of a practitioner's level of skill, experience, and knowledge, and the progression is usually sequential.

When someone achieves a 1st Dan, they have reached an important milestone, and moving to 2nd Dan signifies a deeper understanding and further development in their martial art practice. Each Dan rank often requires additional training, tested techniques, and sometimes teaching experiences, which contribute to the practitioner's skill set.

While the terms "2nd Degree" or other numerical ranks (like 3rd Dan, 4th Dan) exist, they represent different concepts or levels beyond 1st Dan. However, the progression explicitly follows the numerical Dan ranking system, and therefore "2nd Dan" is the accurate descriptor for the rank immediately succeeding 1st Dan.